Problem: $v(t) = (10\cos(t), 10\sin(t), 100 - t)$ What is the velocity of $v(t)$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $(-10\sin(t), 10\cos(t), -1)$ (Choice B) B $(10\cos(t), 10\sin(t), -1)$ (Choice C) C $\sqrt{101}$ (Choice D) D $10\sqrt{2}$
Answer: The velocity of a parametric curve is the derivative of its position. If $f(t) = (a(t), b(t), c(t))$, then the velocity is: $f'(t) = (a'(t), b'(t), c'(t))$ Our position function here is $v(t)$. $v'(t) = (-10\sin(t), 10\cos(t), -1)$ Therefore, the velocity of $v(t)$ is $(-10\sin(t), 10\cos(t), -1)$.